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Center Manifolds for Homoclinic Solutions [PDF]
, 1995 In this article, center-manifold theory is developed for homoclinic solutions of ordinary differential equations or semilinear parabolic equations. A center manifold along a homoclinic solution is a locally invariant manifold containing all solutions ...
Sandstede, Björn, Björn Sandstede
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Are physiological oscillations physiological?
The Journal of Physiology, Volume 604, Issue 9, Page 3672-3693, 1 May 2026.Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
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Homoclinic bifurcation in Chua's circuit [PDF]
, 2005 We report our experimental observations of the Shil'nikov-type homoclinic chaos in asymmetry-induced Chua's oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcations.
Dana, SK +6 more
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Dynamics of a plant-herbivore model with a chemically-mediated numerical response
Mathematics in Applied Sciences and Engineering, 2021 A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modified numerical response.
Lin Wang, James Watmough, Fang Yu
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The Generalized Homoclinic Bifurcation
Journal of Differential Equations, 1994 The author considers a family \(X_ \lambda\) of vector fields that has at \(\lambda= 0\) a homoclinic loop of multiplicity \(n\). The aim of the paper is to present conditions of the versality of \(X\) in a neighborhood of the loop. For this, the author uses the representation of the displacement function given by \textit{R. Roussarie} [Bol. Soc. Bras.
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity coefficients are nonlinear smooth, positive functions of the specific volume, making the system the most ...
Raffaele Folino +2 more
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Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
Abstract and Applied Analysis, 2013 We investigate the Shilnikov sense homoclinicity in a 3D system and consider the dynamical behaviors in vicinity of the principal homoclinic orbit emerging from a third order simplified system.
Gen Ge, Wang Wei
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Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential
Entropy, 2017 In this paper, we study the existence of homoclinic solutions for the fractional Hamiltonian systems with left and right Liouville–Weyl derivatives. We establish some new results concerning the existence and multiplicity of homoclinic solutions for the ...
Neamat Nyamoradi +3 more
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We investigate the existence and spectral stability of traveling wave solutions for a class of fourth‐order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization problem, we establish the existence of smooth, exponentially decaying traveling wave profiles for wavespeeds
Vishnu Iyer +2 more
wiley +1 more source
Multibump solutions for an almost periodically forced singular Hamiltonian system
Electronic Journal of Differential Equations, 1995 existence of so-called multibump homoclinic solutions for a family of singular Hamiltonian systems in $R^2$ which are subjected to almost periodic forcing in time.
Paul H. Rabinowitz
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